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A113276
Decimal expansion of de Bruijn's constant.
0
1, 1, 0, 6, 4, 9, 5, 7, 7, 1, 4
OFFSET
1,4
COMMENTS
From Amiram Eldar, Jun 22 2021: (Start)
The minimal number c such that for any sequence of nonnegative numbers b(k) the following inequality always holds: Sum_{k>=1} b(k) <= c * Sum_{k>=1} sqrt(Sum_{i>=k} b(i)^2/k).
Also called the Copson-de Bruijn constant after the British mathematician Edward Thomas Copson (1901-1980) and the Dutch mathematician Nicolaas Govert de Bruijn (1918-2012). (End)
REFERENCES
R. P. Boas and N. G. de Bruijn, Solution for problem 83, Wiskundige Opgaven met de Oplossingen, Vol. 20 (1957), pp. 2-4.
N. G. de Bruijn, Asymptotic Methods in Analysis, New York: Dover, 1981. See p. 174.
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 217-219.
LINKS
E. T. Copson, Note on Series of Positive Terms, J. London Math. Soc., Vol. 2 (1927), pp. 9-12.
E. T. Copson, Note on Series of Positive Terms, J. London Math. Soc., Vol. 3 (1928), pp. 49-51.
Eric Weisstein's World of Mathematics, de Bruijn Constant.
EXAMPLE
1.1064957714...
CROSSREFS
Sequence in context: A333322 A348896 A153630 * A086034 A191622 A021943
KEYWORD
nonn,cons,hard,more
AUTHOR
Eric W. Weisstein, Oct 21 2005
STATUS
approved